Guy Even, Joseph Naor, et al.
Journal of the ACM
Given an integer k, and an arbitrary integer greater than {Mathematical expression}, we prove a tight bound of {Mathematical expression} on the time required to compute {Mathematical expression} with operations {+, -, *, /, ⌊·⌋, ≤}, and constants {0, 1}. In contrast, when the floor operation is not available this computation requires Ω(k) time. Using the upper bound, we give an {Mathematical expression} time algorithm for computing ⌊log log a⌋, for all n-bit integers a. This upper bound matches the lower bound for computing this function given by Mansour, Schieber, and Tiwari. To the best of our knowledge these are the first non-constant tight bounds for computations involving the floor operation. © 1992 Birkhäuser Verlag.
Guy Even, Joseph Naor, et al.
Journal of the ACM
Moses Charikar, Joseph Seffi Naor, et al.
IEEE/ACM Transactions on Networking
Arturs Backurs, Piotr Indyk, et al.
ICML 2019
Lawrence L Larmore, Baruch Schieber
Journal of Algorithms